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Univariate Statistics 9/18/2012

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Readings Chapter 2 Measuring and Describing Variables (Pollock) (pp.32-33) Chapter 2 Descriptive Statistics (Pollock Workbook) Homework: Chapter 1 Introduction to SPSS (Pollock Workbook) – Question 1 Parts A &B – Question 2

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About the Homework It must be turned in during class. It cannot be emailed It must appear on the workbook paper (original or a photocopy) You cannot:

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OPPORTUNITIES TO DISCUSS COURSE CONTENT

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Office Hours For the Week When – Weds and Fri 11-1 – Thursday 8-12 – And appointment

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Course Learning Objectives Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data. Students will achieve competency in conducting statistical data analysis using the SPSS software program.

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Variables

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Measured Concepts We need to operationalize concepts to test hypotheses

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Four Categories of Variables

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Categorical Nominal Name And provide value Ordinal Name Provide value And Order

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CONTINUOUS VARIABLES

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What about them The values matter Your variable includes all possible values, not just the one’s that you assign. Name, order, and the distances between values matter.

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Interval Level Variables The values matter at this level The distances matter The zero is arbitrary

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Examples of Interval Scales

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Ratio Variables The Full properties of numbers A zero means the absence of a property Classify, order, set units of distance

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Examples

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Lets Look at this one again

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DESCRIPTIVE STATISTICS

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Descriptive Statistics These simply describe the attributes of a single variable. You cannot test here (you need two variables) Why do them?

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Categories of Descriptive Statistics Measures of Central Tendency The most common, the middle, the average Mean, Median and Mode Measures of Dispersion How wide is our range of data, how close to the middle are the values distributed Range, Variance, Standard Deviation

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Frequency Distributions This Provides counts and percentages (relative frequencies) of the values for a given variable Computing a relative Frequency The Cumulative Percent is percentage of observations less than or equal to the category

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Examples St. Edward’s Data

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The Mode the most frequent observation of the variable in a distribution Which category is most common There can be more than 1

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Examples What are the Modes here? 1.110,105.100.100.100.100.99.98 2.110.105.105.105.100.95.95.95.90

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Advantages and Disadvantages Advantages of the Mode Disadvantages of the Mode

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Where Parties Should Go in A Normal Distribution They Move To the Center, why?

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What About A Bimodal Distribution?

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Party Polarization

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A polymodal System

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THE MEDIAN

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The Median It only tells us one thing the value that lies in the middle of the data when arranged in ascending order.

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Examples The University of TexasTexas The 78704 Zip Code

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Examples The middle observation = (N+1)/2 Characteristics and problems of the median Three Examples – (133,113,112,95,94) – (27,12,78,104,45,34) – (105,102,101,92,91,80)

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Locating the Median

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Finding the Median location of median case (1747+1)/2 = 874 Where Does that case fall? – Case 1 through 534 = has value of 0 – Case 535 through 1747 = has value of 1 Case 874 is more than 535 and less than 1747 THE MEDIAN IS 1, the category is voted You can also look here for where 50% falls

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Lets Try Again

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Median Voter Theory

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THE MEAN

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The Mean What is it How do you compute it?

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About the Mean Characteristics of the Mean Problems of the Mean

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An Example NameIncome Skipper50.00 Gilligan150.00 Mary Ann150.00 Professor400.00 Mrs. Howell500.00 Mr. Howell1000.00 Ginger3000.00

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Picking the Right Measure MeasureLevel of Analysis ModeNominal, Ordinal, Ratio, Interval MedianOrdinal, Ratio, Interval MeanRatio, interval (sometimes ordinal)

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Measures of Dispersion 9/24/2013. Readings Chapter 2 Measuring and Describing Variables (Pollock) (pp.37-44) Chapter 6. Foundations of Statistical Inference.

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